Chalcogenide Letters
Vol. 11, No. 6, June 2014, p. 257 - 263
ELECTRONIC STRUCTURE AND OPTICAL PROPERTIES OF QUATERNARY CHALCOGENIDES AgIn0.5Ga0.5Se2 AND CuIn0.5Ga0.5Se2 BY FIRST-PRINCIPLES CALCULATIONS S. R. ZHANGa*, S. F. ZHUb , H. J. HOUc, L. H. XIEd, S. H. XIANGa, K. H. SONGa a Department of Physics and Information Engineering, Huaihua University, Hunan 418008, China b Department of Materials Science, Sichuan University, Chengdu 610064, China c School of Materials Engineering, Yancheng Institute of Technology, Jiangsu 224051, China d Institute of Solid State Physics & School of Physics and Electronic Engineering, Sichuan Normal University, Chengdu 610066, China
In this work, by performing first principles calculations within generalized gradient approximation (GGA) based on Density Functional Theory (DFT), the band structure and optical-related properties of quaternary metal chalcogenides AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2 are presented. The energy gap is found to be direct of 0.177 and 0.011 eV for the two materials, respectively. The differences of the complex dielectric functions, the absorption spectra and the reflectivity coefficients of AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2 are discussed. It follows that the electronic configurations of monovalent X (X = Ag, Cu) cations are responsible for the different electronic and optical properties of XIn0.5Ga0.5Se2. (Received April 21, 2014; Accepted June 3, 2014) Keywords: AgIn1-xGaxSe2, CuIn1-xGaxSe2, The first principles, Electronic properties, Optical properties
1. Introduction Recently, a number of ternary and quaternary semiconductors of type I-III-IV2 (I = Cu, Ag; III = Al, Ga, In; IV=S, Se, Te) crystallized in the chalcopyrite structure have attracted considerable interest of researchers due to their optoelectronic properties appropriate for designing nonlinear optical devices and solar cells [1-4], especially CuIn1-xGaxSe2 (CIGS) was expected to be useful in solar cell applications because it has large absorption coefficients at the band gap energy[5-9], and AgIn1-xGaxSe2 was used as materials for laser-frequency doublers for the mid-IR spectral reion owing to the nonlinear properties[10-13]. A typical representative of this family, CuIn0.5Ga0.5Se2 has been widely studied. In experiments, the various interesting properties including the structure character[14-18], electronic structures[16-20], and optical constants[17, 18, 20, 21] have been investigated. The corresponding theoretical work, such as electronic structures and optical constants[22, 23], also has been followed. However, the experimental studies on the precise material characterizations of the AgIn0.5Ga0.5Se2 crystals concern the structure properties[12, 24], electronic and optical properties[25, 26] are still rather limited, and no theoretical work has been reported in comparison with other chalcopyrite semiconductors. *
Corresponding author:
[email protected]
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In this paper, our motivation is to discuss the effect of monovalent cations on the electronic behaviors of AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2 quaternary chalcopyrite crystals, we carry out this task by calculating the structural, electronic, and optical properties of these chalcopyrite compounds on the first principles basis. 2. Computational methods The calculations are performed in the framework of density function theory. Advanced plane wave expansion technology is applied to optimize the lattice constants and calculate the electronic and optical properties of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 using the CASTEP computer code [27]. The effects of exchange–correlation interaction are treated with the generalized gradient approximation (GGA) of Perdrew-Burke-Ernzerh [28], known as PBE-GGA. The Vanderbilt-type ultrasoft pseudopotentials (USP) [29] are employed to describe the electron–ion interactions. A plane-wave cutoff energy of 400.00 eV in USP was employed throughout the calculation. For the Brillouin-zone sampling, the electronic structures used 4×4×2 k-points grid generated according to the Monkhorst–Pack scheme. In the calculations of the optical susceptibilities, a dense mesh of uniformly distributed k-points is required. Hence, we have used 8×8×4 meshes to calculate the complex dielectric functions of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2. The calculations assured a very high level convergence with respect to all parameters: the total energy difference within 1.0x10-6 eV/atom, the maximum Hellmann–Feynaman force within 0.01 eV/Å, the maximum stress within 0.02GPa and the maximum atom displacement within 1.0x10-4Å. 3. Results and discussions 3.1 Structure properties The crystal structures of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 belong to I-III-IV2 chalcopyrites with the space group I 4 2d , which are analogous to the widely studied zinc blend structure. The ions positions can be generated using the following minimum set of (x, y, z) coordinates expressed in units of the a an c constants: Group II: (0, 0, 0), (0, 1/2, 1/4), Group IV: (0, 0, 1/2), (0, 1/2, 3/4), Group V: (u, 1/4, 1/8), (-u, 3/4, 1/8), (3/4, u, 7/8), (1/4, -u, 7/8). Here, a is the lattice constant in the x or y direction, c is the lattice constant in the z direction, u is the positional parameter of the Se atoms in the unit cell. The difference between u and 0.25 represents the magnitude of the anions displaced from the ideal tetrahedral site. We used the experimental lattice parameters as a starting point for geometry optimization. The calculated lattice parameters a and c, along with the internal parameter u are compared to experimental data reported in the literature in Table 1. The lattice parameters are found to be 5.693, 11.431 Å and 6.058, 11.624 Å for CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 alloys, respectively. The lattice constant increases when the Cu ions be replaced by Ag ions for CuIn0.5Ga0.5Se2 alloy, it can be reasonable explained by the bigger radius of Ag ions compare to Cu ions.
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Table 1. Calculated lattice parameters(Å)of AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2 as compared to experimental data.
Present a 6.058 c 11.624 u 0.2663
AgIn0.5Ga0.5Se2 experiment a 6.030 6.047c 6.043d 11.26a 11.275c 11.30d 0.2737b 0.2852c
Present 5.693 11.431 0.2316
CuIn0.5Ga0.5Se2 experiment e 5.67 5.6924g 5.72h 11.32e 11.30h 0.24f 0.2438g
a Ref. [12]. b Ref. [11]. c Ref. [24]. d Ref. [26]. e Ref. [15]. f Ref. [14]. g Ref. [17]. h Ref. [18]. 3.2. Electronic properties We have predicted the band structure for CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 along the high symmetry directions in the first Brillouin zone and corresponding projected density of states(PDOS) from the calculated equilibrium lattice constants. The bands and PDOS graphs are given in Fig. 1 and Fig. 2, respectively. For the two alloys, the calculated band structures are similar to each other. Both the two mixed crystals have a direct band gap at the Γ point, and the obtained band gap values are 0.011 eV and 0.177 eV for CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2, respectively. The band gaps are smaller than the experimental values[23, 26], this error is caused by the discontinuity of exchange-correlation energy [30]. From the band structure graph, it exists an energy gap about 0.93 eV in the upper valence band for CuIn0.5Ga0.5Se2 alloy while AgIn0.5Ga0.5Se2 does not, this energy gap may cause strong optical absorption naturally. The partial density of states(PDOS) plays vital role to explain the physical properties of semiconductor. The PDOS for Ag-s/p/d or Cu-s/p/d, Ga-s/p/d, In-s/p/d, Se-s/p for AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2 are shown in Fig. 2, which signify the origin of valence band and conduction band lies in local atomic states of constituent atoms. The Fermi energy is set to zero. The conduction bands for the two alloys are mainly derived from In-s/p and Ga-s/p states and sufficient contribution from Se-s/p states. The valence bands region of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 lies between -15.45 eV to Fermi energy level (EF). The low-energy set of valence band ranging from -15.45 to -12.81 eV is mainly due to d orbitals of In and Ga atoms with an admixture of Se-s states, and the d orbitals of In and Ga atoms are highly localized. In the energy ranging from -5 to 0 eV, the AgIn0.5Ga0.5Se2 alloy exits continuous upper valence bands mostly formed by Ag-d states and p states of In, Ga, and Se atoms, while the CuIn0.5Ga0.5Se2 alloy possesses an energy gap in the region from -2.06 to -2.99 eV, this difference is mainly due to the Cu-d states and the p state of In, Ga, and Se atoms don’t exit in this energy range.
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Fig. 1. Calculated band structure of CuIn0.5Ga0.5Se2 (a) and AgIn0.5Ga0.5Se2 (b).
Fig. 2. Projected density of states for AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2.
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3.3 Optical properties We now consider the optical properties of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2. The dielectric function ( ) 1 ( ) i 2 ( ) can be used to describe the linear response of the system to electromagnetic radiation, which relates to the interaction of photons with electrons. The real 1 ( ) and imaginary part 2 ( ) of the dielectric functions are calculated using the usual Kramers–Kronig relationship[31]. Other optical properties, such as reflectivity spectra R ( ) , absorption coefficient ( ) , can be derived from the complex dielectric function. For the calculations of optical properties, by using the scissors operator, we have corrected our band gap values with 1.33 eV for CuIn0.5Ga0.5Se2 and 1.4 eV for AgIn0.5Ga0.5Se2, respectively. The optical functions calculated by neglecting all lattice vibrational effects and pertaining only the electronic transitions are shown in Fig. 3-Fig. 5. The average of complex dielectric functions are presented in Fig. 3. The main shape of the real parts of these complex dielectric functions of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 are similar. The static dielectric constants 1 (0) , calculated at the equilibrium lattice constants, are about 9.68 and 7.12, respectively. The calculated imaginary parts of the frequency-dependent linear dielectric function are different obviously. For CuIn0.5Ga0.5Se2 the main peaks position locate around 2.62 and 6.08 eV, respectively. For AgIn0.5Ga0.5Se the main peak position locates around 6.72 eV. These peaks correspond to the optical transitions from the valence band to the conduction band.
Fig.3. Dielectric functions for AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2.
The absorption spectra are shown in Fig.4. For the two interesting materials, according to the graph, it is obvious that the shape of the curves of absorption spectra are similar, and the absorption coefficients decrease rapidly in the low-energy region, which is the representative character of the semiconductor and insulator. One can see that CuIn0.5Ga0.5Se2 alloy has a higher absorption than AgIn0.5Ga0.5Se2 in the 0 -5 eV region, the main visible sunlight spectrum could be possible to be absorbed. This results are similar to the earlier measurements [32]. In Fig.5, we present the calculated optical reflectivity spectra of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 crystal, there is a reflectivity peak for both two materials at 2.4 eV around, it is mainly caused by the
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transition from Se-4p to Cu-3d. In 0-5 eV region, especially in the infrared and visible light region, we found that, the reflectivity of AgIn0.5Ga0.5Se2 is lower compared to CuIn0.5Ga0.5Se2, the calculated reflectivity increases slowly only from 20.6% to 24.8% with the photon energy in the infrared area for AgIn0.5Ga0.5Se2. So, from the absorption and reflectivity spectra, one can draw a conclusion that the transmission of AgIn0.5Ga0.5Se2 is higher and it is a more excellent IR material for making nonlinear optical device, while the absorption of CuIn0.5Ga0.5Se2 is higher and it is a more outstanding material for solar energy.
Fig.4. Absorption spectra of AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2.
Fig.5. Reflectivity spectra of AgIn0.5Ga0.5Se2 and CuIn0.5Ga0.5Se2.
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4. Conclusions In summary, we have presented the structural, electronic and optical properties of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 alloys using the first principles methods. The studied alloys are both characterized by direct band gap materials at the Γ point. Specifically, the difference of the energy band structure and the PDOS between the two interesting materials has been discussed. Also, the different electronic properties of CuIn0.5Ga0.5Se2 and AgIn0.5Ga0.5Se2 lead to their different optical properties. The investigations show that AgIn0.5Ga0.5Se2 is a more excellent IR crystal material than CuIn0.5Ga0.5Se2 for making nonlinear optical device, while the latter is a more outstanding material for solar energy. It is hoped that the present findings may provide reliable data for producing optoelectronic devices.
Acknowledgments This work was supported by National Natural Science Foundation of China under Grant No.11174100, and Key project of Hunan provincial Natural Science Foundation under Grant No.11JJ2003, and the project of Hunan provincial Education Department, China under Grant No.13C711. References [1] L. S. Lerner, J. Phys. Chem. Solids 27, 1 (1966). [2] D. C. Hanna, V. V. Rampal, R. C. Smith, Opt. Commun. 8, 151, (1973). [3] R. C. Eckardt, Y. X. Fan, R. L. Byer, C. L. Marquardt, M. E. Storm and L. Esterowitz, Appl. Phys. Lett. 49, 608 (1986). [4] A. Rockett and R. W. Birkmire, J. Appl. Phys. 70, R81 (1991). [5] S. H. Wei, A. Zunger, J. Appl. Phys. 78, 3846 (1995). [6] R. Caballero, C. Guillén, M. T. Gutiérrez and C. A. Kaufmann, Progress in Photovoltaics: Research and Applications 14, 145 (2006). [7] M. A. Contreras1, Brian Egaas, K. Ramanathan, J. Hiltner, A. Swartzlander, F. Hasoon and R.Noufi, Progress in Photovoltaics: Research and Applications 7, 311 (1999). [8] M. J. Romero, K. Ramanathan, M. A. Contreras, et al., Appl. Phys. Lett. 83, 4770 (2003). [9] Y. Tani, K. Sato, H. Katayama-Yoshida, Appl. Phys. Express 3, 101201, (2010). [10] Yu. M. Andreev, P. Geiko, V. Voevodin, et al., Jpn. J. Apll. Phys. 39, 94 (2000). [11] V. V. Badikov, V. I. Chizhikov, V. B. Laptev, V. L. Panyutin, G. S. Shevyrdyaeva, S. I. Scherbakov, Proceedings of SPIE 140, 4972 (2003). [12] K. Yoshino, H. Komaki, K. Itani, S. F. Chichibu, Y. Akaki, T. Ikari, J. Cryst. Growth 236, 257 (2002). [13] Shuquan Wan, Shifu Zhu, Beijun Zhao, Baojun Chen, Zhiyu He, Jianhua Xu, J. Cryst. Growth 318, 713 (2011). [14] D. K. Suri, K. C. Nagpal, G. K. Chadha, J. Appl. Cryst. 22, 578 (1989). [15] D. Aldakov, A. Lefrançois and P. Reiss, J. Mater. Chem. C 1, 3756 (2013). [16] K. T. R. Reddy, R. B. V. Chalapathy, Sol. Energy Mat. Sol. Cells. 50, 19 (1998). [17] R. Dĺaz, J. Vac. Sci. Technol. A 19, 2407 (2001). [18] B. A. Masour, I. K. El Zawawi, H. Shaban, Journal of Materials Science: Materials in Electronics 14, 63 (2003).
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